Quantum ML models can perform quantum data processing on multiple copies of quantum states. For product states, we only perform the following procedure.
For each repetition, we perform two-copy Bell basis measurements on \(\rho \otimes \rho \)  to simultaneously measure \(X\otimes X, Y \otimes Y, Z \otimes Z\)  on each of the \(n\)  qubits in \(\rho \) .
We can determine the eigenbasis (X-basis, Y-basis, or Z-basis) of each qubit when we found that two of the observables \(X\otimes X, Y \otimes Y, Z \otimes Z\)  result in both \(\pm 1\)  outcomes.
For two of the three observables, the underlying distribution is uniform in \(\pm 1\) , while deterministic outcomes are produced in the third observable.
Since we know the stabilizer bases for each qubit after a few two-copy measurements, we simply measure the \(n\)  qubits in the corresponding stabilizer basis on the final copy to recover the full state.
We refer to [1]}, [2]}, [3]}, [4]} for results on efficient procedures for testing and learning stabilizer states in general.
